Question

The volume of a cuboid is $\mathbf{1536}\mathbf{}{\mathit{m}}^{\mathbf{3}}$. Its length is $\mathbf{16}\mathbf{}\mathit{m}$ and its breadth and height are in the ratio $\mathbf{3}\mathbf{:}\mathbf{2}$. Find the breadth and height of the cuboid.

Answer 1

Step 1: Find the value of $x$

Given,

Volume of a cuboid $=1536m^3$

Length $\left(l\right)$ of a cuboid $l=16m$

The ratio of breadth $\left(b\right)$ and height $\left(h\right)$ of a cuboid $=3:2$

Let be consider $b=3x$ and $h=2x$.

Volume of cuboid $=l\times b\times h$

$1536=16\times 3x\times 2x$

$1536=96x^2$

$x^2=\frac{1536}{96}$

$x^2=16$

Taking square root on both sides

$x=\sqrt{16}$ $\left(\because 4^2=16\right)$

$\therefore x=4$

Step 2: Substitute the value of $x$

$b=3x=3\left(4\right)=12m$

$h=2x=2\left(4\right)=8m$

$\therefore$The breadth and height of the cuboid are $12m$ and $8m$ respectively.